No supermarket has their own food factories. All of their products are purchased from the same places that supply many of the well-known brand names. That could mean the same quality, higher quality or lower quality, depending upon the criteria set by each supermarket.
For example, the first job I ever worked in (between 5th form and 6th form, or Year 11 and Year 12 if you're younger than me!) was in a pork pie factory. Most of the production was under the company's own name (Harris Pork Pies) but they also made pork pies for Marks and Spencers. The quality of the M&S pies was of a higher quality than the 'normal' production.
Similarly, I did a student job working at a firm which produced frozen sliced green beans. None of the beans left the plant with the name of the factory (Christian Salvesen) on the packaging. They were bagged as products from 'Ross', 'Findus', 'Spar',etc. They were the SAME beans, from the SAME farms, processed in the SAME way, irrespective of the packaging. The only difference was that the beans for the cheaper brand labels went through a slightly less rigorous sorting process (to remove stray bits of bean plants) than the dearer products did.
Depending upon the criteria set by each supermarket, for each product, some supermarket 'own brands' will be BETTER than the 'branded' products. Others will be exactly the same, whereas some (particularly with 'value' labelling) might be slightly inferior. It's up to customers to decide what is best for them by actually tasting, or using, the product, rather than looking for a brand name.
Chris